This thesis develops a new methodological approach to test for threshold cointegration. It determines the threshold locations, the number of thresholds, and tests the null hypothesis of a unit root against the alternative of a stationary threshold process using p-values based on a residual-based block bootstrap for the nonlinear threshold autoregressive specification (TAR). Chapter 2 describes the methodological approach which combines Gonzalo and Pitarakis (2002) and Seo (2008). Chapter 3 employs Monte Carlo analysis to investigate the properties of the new approach. The results indicate that the methodology performs well and is suited for application to real world time series. Chapter 4 applies the new approach in combination with a threshold error correction model (ECM) to determine the spatial relationships among three crude oil prices: WTI, Brent, and Oman, from 2008 through 2011. The results indicate that the crude oil benchmarks are tied together by a long run relationship; however, the recent reversal in price premium between the two main crude oil benchmarks, WTI and Brent, is an anomaly that has resulted in a time period in which the series do not have a tendency to move back toward their long run relationship. Chapter 5 applies the new approach, in combination with threshold ECMs, with regime switches being triggered by the upstream markup margin to determine the vertical relationships between the crude oil, rack, and retail gasoline prices for six cities across North America. The results using both daily and weekly data between 2008 and 2011 suggest that upstream and downstream prices are cointegrated. There is evidence of band-TAR in which the crude, rack, and retail prices are free to diverge until the markup margin is squeezed or stretched beyond a lower or upper threshold. This suggests that abnormally high margins cannot be sustained indefinitely. The threshold ECMs indicate that there is no systematic relationship between the speed of adjustment and the markup margin; however, the residuals exhibit a leverage effect in which volatility and price changes are negatively correlated. Chapter 6 concludes with a summary of Chapters 2 through 5 and makes suggestions for future research.